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LIBRA FLY OF THE U N IVER.5ITY Of ILLI NOIS 621.365 Ije655te no. 40-49 cop. 2 Digitized by the Internet Archive in 2013 http://archive.org/details/studyofchromatic48loyt ANTENNA LABORATORY Technical Report No. 48 A STUDY OF CHROMATIC ABERRATION OF A COMA -CORRECTED ZONED MIRROR by Dr. Y. T. Lo Contract AF33 (616) -6079 Project No. 9-(13-6278) Task 40572 Sponsored by. WRIGHT AIR DEVELOPMENT DIVISION Electrical Engineering Research Laboratory Engineering Experiment Station University of Illinois Urbana, Illinois 3fc5 f.ff ENGINEERING LIBRARY ACKNOWLEDGMENT It is a pleasure to acknowledge the comments on the manuscr]p T f this report gnen by Professors G, A Deschamps and P E Mayes CONTENTS Page 1„ Introduction 1 2. Results and Discussions 4 3. Simplified Analysis 18 Conclusion 28 Reference 29 ILLUSTRATIONS Figure Number Page 1. Cross-section of a zoned mirror 2 2„ Image pattern on the focal plane for a = 6 3„ Image pattern on the focal plane for a = 5° 7 4. Image pattern on the focal plane for a = 10° 8 5„ Image pattern on the focal plane for a = 15 9 6. Image paMprn on the focal plane for a = 20° 10 7 a) maximum field intensity of the image vs the angle of incidence a, b) variation of directive gain vs scan angle for the designed frequency f and 1.0625 f 12 o o 8„ Relation between the position of off-axis feed and beam deflection angle a at 1„0625 f 13 o 9. Ratio of the two first secondary maxima vs scan angle a for the designed frequency f and 1.0625 f 14 10. Magni + ude of secondary maximum vs its position in the focal plane for the designed frequency f and 1.0625 f 16 o o 11, Geometry cf a typical zone of the mirror 19 1 . INTRODUCTION Briefly, a zoned mirror consists of sections of a set of confocal parabolas with focus at c and axis VC, defined by P=2(f-nX./2)/(l+cos4 J ), n = 0, 1, 2, ... where f is the focal length of the parabola with the largest focal length as shown in Figure 1 „ This family of parabolas intersect the circle 2 with center also at C and radius f at V , P , P„.c « 1 1 2 If a set of parallel planes perpendicular to the axis VC are drawn through the vertices N , N„, N„, „ „ „ of the parabolas, they will intersect the 1' 2 3' circle at Q , Q , Q , „ . , The sections of the parabolas cut out by the lines parallel to VC and passing through Q , Q , Q , » . . form a zoned mirror as shown by the solid line in Figure 1„ 1 In a previous report the properties of such a coma-corrected zoned mirror are investigated by diffraction theory. The image pattern for various incident angles of a plane electromagnetic wave and also the radiation characteristics of the system are evaluated numerically by means of simple fundamental functions and Fresnel integrals, It is concluded that for a mirror with small F-number and nearly uniform illumination the zoned mirror shows great effectiveness in coma correction. Since for such a two- dimensional cylindric mirror there is no spherical aberration and astigmatism, the only important defect of this system will be the chromatic aberration. Unfortunately, such a system is inherently very frequency-sensitive; moreover, to this author s knowledge there is yet no method available for chromatic correction of this system. However, in contrast to many optical systems a microwave device even with a limited bandwidth usually finds very wide applications In this investigation the image pattern deterioration due to chromatic aberration is studied. The purpose of this short report is to / B 2^ 2 - Figure i. Cross-section of a zoned mirror supplement some of the information on this point which is not found in the previous report. 2, RESULTS AND DISCISSIONS Diffraction theory was used in the previous *ork c 1 nee coma aberrati >n has a dominant effect on the minor lobes where the usual hirchhoff approximation is generally susceptible to larger error However the results sho* that the contribution to trie image field due to the coupling current? among zones is negligible in comparison with that due to the geometric optics current induced by an incident plane wave, Moreover. t he edge diffract. on effect is also of higher order as compared to the latter (except at nulls and small minor lobes), However, with considerable chromatic aoerration the lower order contribution becomes appreciable (the nulls oi 'he pattern will be filled up and the minor lobe level will be raised) therefore, tne above mentioned high order effects become less significant when the mirror is operated at a frequency other than that of proper design In such a case the previously established theory'can be greatly simplified, since it requires no near-field solution which is only essential in the evaluation of coupling effed between zones, Such a simplified theory will be established and discussed in the next section However., this theory is not used here to evaluate the deterioration of the patterns =ince a program for the ILLIAC (the electronic computer at the University of UlinoJ ) based upon the more rigorous approach ha? already been established th< previous investigation. With only a minor modification this idapted to the evaluation of the performance of a zoned dimensions at frequences equal to 1 0625 I o i ! (a) F-number = f/D = 0.556, (b) the focal length = f 10\ where X. is the wavelength corresponding to the design frequency f ; (c) total number of zones = 11. For the purpose of comparison, the performance of an equivalent smooth parabola (one with same focal length and aperture) is also computed. As expected the latter by comparison is a wide-band device since the only effect of changing frequency is to vary the aperture dimension in wavelength accord- ingly. Figures 2 and 6 show the image pattern in the focal plane for an incoming o o o o o plane wave with incident angle equal to , 5 , 10 , 15 , and 20 with respect ' to the axis of the system. By comparing these patterns with those at the design frequency f , it is seen that at a frequency deviated by 6.25 7c from f the image patterns are changed considerably. First of all the pair of minor lobes adjacent to the major beam are no longer distinct; instead they are merged with the major lobe. This is evidently a result of overwhelming chromatic aberration. However, it is interesting to see that other minor lobes seem to be comparatively less affected by this aberration and also that the symmetry of the image pattern is maintained up to an incident angle equal to 10° „ For the smooth parabola, the image patterns remain very much the same as those at the design frequency f Q , except that the beamwidths are somewhat smaller and the gain is slightly higher up to a scan angle o. = 10 f this being a consequence of an increment in aperture as referred to wavelength. However, this is no longer true for large scan angle since a <0 *> ^ ro cvj (AJLISN31NI 01313 3AllV13d) z 3 W II d u o 0) be E (A1ISN31NI Cl~l3ld 3AI1V1V13U) z 3 (A1ISN31NI 01313 3AI1V13U) Z 3 to u o 0) c ca 0) U a be in <fr ro cj (A1ISN31NI 01313 3/VI±V13H) Z 3 X sr ro cj (A1ISN31NI Q13IJ 3AllVH3d) z 3 11 system of wider aperture has larger aberrations. These results can be seen in Figure 6 which also shows the maximum field intensity (equivalent to the gain except for a proportionality constant) and the normalized gain (referred to the gain at a = 0) against the scan angle a for both mirrors at frequencies f and 1.0625 f . o o It is seen from Figure 7(a) that the loss in gain of the zoned mirror due to 6.25% increment in frequency is from 1 db at a = to about 2 db at a = 20 . Figure 7(b) also shows that the gain at this frequency drops at a faster rate than that at f as the scan angle a increases (somewhat close o to that of the smooth parabola) . Figure 8 shows the relation between the position of the off-axis feed and the beam deflection angle a at 1.0625f . If these curves are compared o with those at f , one finds practically no difference. This fact indicates o that the lateral chromatic aberration of the so-called "diffraction focus" is not severe at all, at least in the range considered. As to the longitudinal chromatic aberration no computation has been done. But as will be seen , later, i a very simple result can be obtained which states that as expressed in*" percentage of the original focal length the longitudinal chromatic aberration is equal to the percent change in wavelength as referred to \> . Since the first pair of minor lobes are not distinct, in other words, the coma aberration is overshadowed by a strong chromatic aberration at this frequency, it becomes meaningless to evaluate the coma in terms of their ratio as has been done previously. However, for the smooth parabola this ratio is shown in Figure 9 at both frequencies together with that for the zone mirror at f . Since a larger ratio indicates a larger coma aberration o this result is in agreement with the fact that a wider aperture (in wavelength) 12 >- (fi UJ f- Q X Ld '■0625 ft x < 10 15 20 SCAN ANGLE oc (DEGREE) < UJ > < _l UJ or 10 15 20 SCAN ANGLE oC (DEGREE) 25 I 7. a) maximum field intensity of the image vs the angle of incidence Q, b) variation of directive gain vs scan angle for the designed frequency f and 1.0625 f o o 13 If) CVJ (0 o ID ro cvj y/ k lN3IAI30V~ldSIQ Q333 s CS XI ■a c 03 T3 CD <H o o C o m •h eg +- 1 to ■H O O ,-i a 0) a! x: i-H bD ce -a 15 suffers more from aberrations. Figure 10 shows the field intensity levels of the first pair of the minor lobes (adjacent to the major beam) vs, their positions in the focal plane of the smooth parabola for an incident wave at frequencies f and o 1.0625f . Also shown in this figure are those of the zoned mirror at f o o only. It may be noted that the side lobe level of an image pattern is not exactly the same thing as that of the corresponding radiation pattern. The purpose of preparing Figure 10 is in an effort to relate these two quantities,, By reciprocity if a feed is at y/^ in the focal plane minor lobes of corresponding intensity as shown in Figure 10 will be produced somewhere in space. At the same time the major lobe field intensity corresponding to this feed displacement can be found by first using Figure 8 to obtain the scan angle # ( or the beam deflection angle in the terminology of transmitting) for this value of y/^ , then referring Figure 7(a) for the intensity. The ratio of these two intensities is the side lobe level of the radiation pattern for the feed at y/^ . Incidentally Figure 10 also shows slightly o higher side lobe levels for the parabola operating at higher frequency, especially at large scan angle. In FiguVes 2 to 6 there are also shown the image patterns of the zoned mirror at a frequency of 1 . 125f . Except the case of normal incidence all images are so blurred" that the major and minor lobes are no longer distinguishable A poor image in this case may be easily explained. At this frequency the field contribution of the outer six zones (although they are narrower in width) will have a component opposite to that due to the central zone for the normal incidence case. On the other hand at a WniNIXVW AUVQN033S JO A1ISN31NI Q13IJ 17 frequency equal to l,0625f , no such negative contribution arises except the outer two narrow zones. If one uses this as a criterion to determine the bandwidth such that no zone contributes a field at focus in opposite sense then the maximum total bandwidth as referred to the frequency f is given by — = .- — where N = total number of zones. For the present mirror f N-l ^ o A f/f = O.lOo No computation for exactly this frequency has been done since this criterion does not necessarily imply only a slight deterioration of the pattern and a small minor lobe which are of primary interest for .scanning purpose. It seems to be safe to infer that for the latter application the bandwidth will be less than the value indicated above. In conclusion, it is seen that from the point of view of the image sharpness, the gain, and side lobe level, the zoned mirror at 1.0625f or higher is worse than a corresponding smooth parabola in scanning ability. A similar conclusion may also be reached on the lower frequency side of f „ 18 3. SIMPLIFIED ANALYSIS Since for the zoned mirror at a frequency different from f , the design frequency, the chromatic aberration becomes so overwhelming, a lower order approximation will provide a fairly accurate solution. In this section such a simplified theory will be given. In Figure 11, a typical zone, (except the central one) is shown *ith a plane wave incident at an angle a with the axis ox. Let the intersection of the zone and the circle be Q (x ' , y' ), a typical point on the strip be QCx', y') , the angle of the strip with respect to the y-axis be T and 0Q o = s > 0Q= s ^ Then the current induced on the strip based upon the infinite plane solution in the previous report . ICQ) = I cos (« + x) e jk S Sin (a + T) Cl) where *1 1 s the intrinsic wave impedance of free space , The f leld intensi ty at observation point P (x,y) is given by E(p) = -i--cos (a + T) f 2 H (2 Hr) e jkS Sin {a + T) ds (2) 2J 7 ! J o S l where s and s are distances of the edges of the strip function origin 1 ^ 0, and f f ' N 2 / / N 2 r = | (x - x) + (y - y) 1/2 In fact this is generally true in optical systems c In systems with large aberrations even geometrical optics gives a good description of the image deterioration, See E Wolf, Rep Prog in Phvsics (London Physical Society) 14, (1954), 95 Also~M BorrTand E„~Wolf , Principles of Opt ics. Chapter IX, 1959, Pergamon Press 19 9-X Figure 11. Geometry of a typical zone of the mirror 2'; Let x ! = x' + x , y' = y' + y o o 2 2 V2 s" = (x- 2 + y" 2 ) r = P Q , o o ' Then 5 = the angle between P Q and the axis x 0. o oo 2 r = r - 2r S" sin T cos 6 + 2r S" cos T sin 6 + S' (3) o o o = r 2 + S*' 2 + 2r S" sin (6 - t) o o For the observation point P in the neighborhood of focus F such that r ^ f >> fS - S)/2, then o 2 1 v m r [1 + S" sin (6 - T)/r ] (4) o o Since we are primarily interested in large aperture which implies that the focal length f is considerably larger than wavelength X^ the Hankel function in the integral can be replaced by its asymptotic expression r~\ m — -, . „,. I „ ■ jkr [1 + s" sin (5 - r)/r H^) ( k r) « PL e -^ + J */4 * /_£L- e J o L o f kr WTTkr Therefore ti o~ /-a T % "Jk[r - S sin (a + T )] f S 2 ., „ w v c os (a + t ) o o J -Jkqs , „ E(p) = ; 07r . , ~ e J „ e J M ds ^ikr -^ s cos fa + Tl -J fc t'o " S o Sin (a + T) ^ ^"^^ - ^^/J^ t| /27Tjkr e (5) where q = sin f6 - t) - sin ( a + t). 21 By assuming that s'' = - s" which is nearly true for most strips (or by redefining the point Q as the center of the strip, not the interaction with o > the coma circle) then ., , /Tcos (a + x) sln < k 1 S 2> -JK[r o - S o sin(a + x)] E<P) = n^ST — e This is equivalent to the field due to an inhomogeneous line source located at Q with a current o o "H kq since q is a function of 6, depending on the coordinates of observation point P. Let, t 5 , q , s , r , and s" (half width of the strip) be those ' n' n' n' on' on' n values for strip number n. The total field at P(x^y) is N /2 cos (a + t ) sin(kq s" ) -jk[ r - s sin (a + t )] *, \ *, , \ ^ n nn on on n J E(p) = E (p) + 2 — e n=-N T] /j77kr on n (g) nj6l where E (p) is the field at P due to the central zone which has been obtained previously. To conform with our present notations, it is rewritten as follows 0, ■* , x /jf~~ f 1 cos(4j/2 + a) -jk[r-f tan iJj/2 (tan i|i/2 cos a + 2 sin a)] ^1 (P) =t\ \ 2 , /Q e v J _ cos 4V2 where = f sec ty/2 + P - 2fp sec \\>/2 cos (9 - i|0 (P,Q) is the polar coordinate of P(x, y) with respect to the focus F and axis FO. 22 20 is the angular aperture of the central zone (parabola) referred to F. For P in the neighborhood of F, f > > P, then 2 r *» f sec 4V2 - p cos (9-4) Let z = tan 4V 2, and the coordinates of P with respect to F be (Ax, y) ; then 2 dz = dLJJ/2 cos i|j/2 cos 4j = (1 - z ) / (1 + z 2 ) 2 2 sin (^ = 2z / (1 + z ) 2 2 cos 4*/2 = 1/(1 + z ) 2 2 2 sin i^/ 2 = z /(I -*- z ) Substituting these quantities into (9), one obtains z v ( \ n h f cos a - z sin a. -jk(p(z) . . . E 1 (p)=2 ^ - / ^ — eJr dz (10) 1 J -Z V 1 4- z where z 2 = tan Q (10) <p(z) = i x-2(f sin a. + y ) z + [f(2-cos a) + A x]z -2f sin a z + f(l-cos a.) z 4 ] „ 2.-1 (11) X (1 + z ) and z 2 = I (X/f - X 2 /4f 2 ) (12) Since this mirror is primarily for large aperture application and also 2 since the smallest F-number is 1/2, then z is a small number given by 2 z < X/4f < V2D << 1 '13) 23 2 For D = 20\, which is about the case computed before, z < 0.025. By introducing this approximation, the integration in (9) can be carried out in terms of basic functions and Fresnel integrals as shown in the following. Now 2 3 4 <P(z) = x-2 (f sin a +y) z + (f + 2 A x-2 cos a )z +2yz -2Axz 5 6 7 -2yz +2Axz +0(z). (14) Since P is in the neighborhood of F, Ax «f or x, and y « f . Further using the condition indicated by (13), one obtains the following approximations: 2 (p(z) » x-2 (f sin a- + y) z + (f + 2Ax-2 cos a) z = A(z + B/2) 2 + (C-B 2 /4) = A U + D where A = f + 2Ax - 2 cos <*■; AB = -2(f sin a. + y) ; (15) AC = x U = z + B/2; D = C - B /4 Similarly the other factor in the integrand of (10) can be approximated as follows, 2 " 1/2 2 (cos a ~ z S in a) (l + z ) -cos a - z sin a - z (cos a)/2 + z 3 (sin a)/2 = P(z) (16) Substituting (U-B/2) for z in P(z), one obtains a polynomial of third degree in U which may be written as 2 3 g(U) =a +bU+ c U+dU (17) when a, b, c, and d can be obtained by comparing (16) with (17). Therefore 24 E l( p) = 2 Jg. e jk ° I <18J where g(U) e JkAU dU, (18a; U = -z + B/2 U = z, + B/2 2 1 (18b; The first term of I is given by .2 U r 2 J l = a J 1 J e JkAU dU = J F( v/kA U ) - F( VkA U ) (19) oo . 2 I IX where the Fresnel integral F(x) = e dx is available in tabulated form, x The second tern of I is given by U I = b 2 J jkAU* jkAU* Ue JkAU dU = £ S Lf e 2 jkA b sin kAz B jkA(z 2 + B 2 /4) ______ e (20) The third term of I is given by I, = C ^ U 2 e^ 1 ' 2 dB = ° 3 , 2jkA 1 ^ UdeJ"" 2 u. 2jkA 2 U 2 [ (Ue JkAU ) U r 2 2 e JkAU dU °1 " u l j jkAU Ff /kAl I 2 J (21) 25 The last term of I is given by U . (" 2 TT 3 jkAU 2 dU = — — I = d J D e J 2jkA . U, U 2 d e JkAU 2jkA U U 2 e jkAU jkAU 2 e J dU 2jkA jkAU 2 jk AU 2 (U 2 e - U x e ± jkAU 2 jkAU^ ) r-r (e - e jkA (22) To sum up the field at P near F is given by Equation (8) in which the field due to the first zone V P> - > /4 * ikD = ' p V P=l P where z i> l 2> V X 4 are given b y (19) to (22) A, B, C } D, are given by (15) U U are given by (18b) and (10a); a, b, c, d are given by (16) and (17). In Equation (8), the focal length of the first zone is practically inde- pendent of frequency; however that of the rest zones for normal incidence can be easily found. In this case by symmetry the focus must lie on the axis. Let P be such a point on the axis with coordinates (Ax, o) . Then by definition 2 2 2 r = f + (Ax) + 2 f (Ax) cos 2t and o Ax 1 Ax 2 A Ax r = f Q + =- cos 2T + - — 7t sin 2T + 9 — - o f 2 * \ f (23) 1" Vt Now the phase function of the field due to the n zone with n^l in Equation 8) becomes for a - CD = k S sin t - k r «. kx' - k f (1 + ^ cos 2*0 . (24) T n on n on However x' = (n-1) *. on o where p = an integer Then kx 7 - k f (1 + . Ax on f = P X o <P = 2 TT (n-1) rfi— -27TP -^ (1 + -^£_ cos 2T) n a. /v j A. \r% Ax = - 2ir(p-n+l) — jr^_ - 2ir p — £— — ~" cos 2T * (25) Let ^ = ^ + d\ then o <P = - 2 tt (p-n+1) (l-d\ X ) - 2 it p *■ /M cos 2t (Ax/f) n o = 2ir(p-n+l) + 2ir(p-n+l) d^\ -2irp C^o/M cos 2T (Ax/f) (26) Putting 2TT(p-n-^l) d\A ■ 2l7p (\yA) COS 2T (Ax/f), then Ax/f = [l - (n-1) / p] sec 2T d\^ o Since x - (n-1) ^ = f(l-cos 2'«") , on o cos 2T _ i _ ( n _D X. /f = l - (n-1) / p, o' Thus the chromatic aberration expressed in fraction of the focal length is glVen by Ax/f = dV* (27) o which is independent of n to the approximations assumed in (24). Therefore the best focal point for all the zones except the central one is at f(l + d^A ) d i a wavelength ^ 4- dV o o 27 It is obvious that the relation (27) also holds for high mode operation when ^ = nA + d^ where m = integer. 28 CONCLUSION A coma-corrected cylindric mirror which has been studied previously for its coma aberration is re-examined for its chromatic aberration. Although such a device can be operated at multiple modes, at each mode it has a narrow frequency bandwidth. At a frequency 6.25% higher than the designed one, there is a slight loss in gain but the side lobes are raised to a very high level. At such a frequency the scanning performance becomes inferior to a corresponding smooth parabolic reflector. At a frequency 12.5% higher than the designed one, the image formation becomes so poor that no focus is generally recognizable. It may be inferred that such a device has a total bandwidth of perhaps only five or six percent, depending on what deterioration can be tolerated on the side lobes. A simplified formula has been obtained for the image field in the neighborhood of the focus. Such a formula will be found particularly useful when the chromatic aberration is large. It may also be used to evaluate the field witn coma aberration at the design frequency if some errors at the minor lobes and nulls are tolerable. Although no computation has hitherto been done to show how close a solution this theory provides, yet it is clear that the major approximation involved is that only the geometric optics current is considered. Even in the absence of chromatic aberration, this has been previously shown to be a close approximat ion. A simple formula of the longitudinal chromatic aberration for the case of normal incidence is obtained. 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' ~~ Contract AF33 (616) -6079 "Use of Coupled Waveguides in a Traveling Wave Scanning Antenna/' Technical Report No 36, R H. MacPhie, 30 April 1959. "On the Solution of a Class of Wiener-Hopf Integral Equations in Finite and Infinite Ranges," Technical Report No. 37, Raj Mittra, 15 May 1959. "Prolate Spheroidal Wave Functions for Electromagnetic Theory/' Technical Report No. 38, W. L, Weeks, 5 June 1959. "Log Periodic Dipole Arrays," Technical Rep ort No. 39, D,E„ Isbell, 1 June 1959, "A Study of the Coma-Corrected Zoned Mirror by Diffraction Theory " Technical Report No. 40, S. Dasgupta and Y. T. Lo, 17 July 1959, "The Radiation Pattern of a Dipole on a Finite Dielectric Sheet," Technical Report No, 41 , K, G, Balmain, 1 August 1959, "The Finite Range Wiener-Hopf Integral Equation and a Boundary Value Problem in a Waveguide," T echnical Report No. 42 , Raj Mittra, 1 October 1959. "impedance Properties of Complementary Mul titerminal Planar Structures," Technical Report No, 43, G. A, Deschamps, 11 November 1959. "On the Synthesis of Strip Sources," Technical Repor t No, 44, Raj Mittra, 4 December 1959. "Numerical Analysis of the Eigenvalue Problem of Waves in Cylindrical Waveguides,' Tech nical Report Jjo ^_45 , C. H. Tang and Y. T. Lo, 11 March 1960. "New Circularly Polarized Frequency Independent Antennas With Conical Beam or Omnidirectional Patterns,'' Technical Report No. 46, J.D c Dyson and P.E, Mayes, 20 June 1960. "Logarithmically Periodic Resonant-V Arrays," Technical Report No. 47, P,E = Mayes and R, L, Carrel, 15 July 1960. ~ Copies" available for a three week loan period. ** Copies no longer available, AF 33(616) -6079 DISTRIBUTION LIST One copy each unless otherwise indicated iCoromander Iright Air Development Center Attn WCOSI, Library fright-Patterson Air Force Base, Ohio Commander FS, Naval Air Test Center Attn: E7-315, Antenna Section Patuxent River, Maryland Chief Bureau Naval Weapons Department of the Navy Attn (RR-13) Washington 25, D.C. -ommander Air Force Missile Test Center Attn, Technical Library Patrick Air Force Base, Florida prector Ballistics Research Lab. Attn Ballistics Measurement Lab. Aberdeen Proving Ground, Maryland "Hice of the Chief Signal Officer Attn.. SIGNET-5 Eng , & Technical Division Washington 25. D,C, Rational Bureau of Standards department of Commerce Attn; Dr , A , G McNish Mungton 25, D.C Iirector • S. 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L, Hufschmidt Librarian 303 A, Pierce Hall Harvard University Cambridge 38. Massachusetts Hoffman Laboratories, Inc. Attn; S, Varian (for Classified) Technical Library (for Unclassified) M F Contract AF33(604)-17231 Los Angeles, California Dr. R, F Hyneman P.O, Box 2097 Mail Station C-152 Building 600 Hughes Ground Systems Group Fullerton, California ITT Laboratories Attn: L. DeRosa M/F Contract AF33(616)-5120 500 Washington Avenue Nutley 10, New Jersey ITT Laboratories A Div. of Int. Tel. & Tel. Corp, Attn: G, S. Giffin, ECM Lab. 3700 E. Pontiac Street Fort Wayne, Indiana Jansky and Bailey, Inc. Engineering Building Attn; Mr. D. C. Ports 1339 Wisconsin Avenue, N.W. Washington, D.C. Jasik Laboratories, Inc. 100 Shames Drive Westbury, New York John Hopkins University Radiation Laboratory Attn; Librarian M/F Contract AF33(616)-68 1315 St. Paul Street Baltimore 2, Maryland Applied Physics Laboratory Johns Hopkins University 8621 Georgia Avenue Silver Spring, Maryland HRB-Singer, I nc Attn Mr R A Evans Science Park State College, Pa , Mr, Dwight Isbell 4620 Sunnyside Seattle 3, Washington Lincoln Laboratories Attn. Document Room M/F Contract AF19(122)-458 Massachusetts Institute of Technology P.O. Box 73 Lexington 73, Massachusetts AF 33(616)-6079 Litton Industries, Inc. Maryland Division Attn,. Engineering Library M F Contract AF33(600)-37292 4900 Calvert Road College Park, Maryland Lockheed Aircraft Corporation Attn; C. D, Johnson M F Contract NOa(s) 55-172 P.O, Box 55 Burbank, California University of Michigan Aeronautical Research Center Attn: Dr, K. Seigel M/F Contract AF30( 602)-1853 Willow Run Airport Ypsilanti, Michigan Microwave Radiation Co., Inc. 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California Philco Corporation Government and Industrial Division Attn: Dr„ Koehler M/F Contract AF33(616)-5325 4700 Wissachickon Avenue Philadelphia 44, Pennsylvania Prof. A, A. Oliner Microwave Research Institute Polytechnic Institute of Brooklyn 55 Johnson Street - Third Floor Brooklyn, New York Radiation, Inc , Technical Library Section Attn Antenna Department M. F Contract AF33(600)-36705 Melbourne, Florida Radio Corporation cf America RCA Laboratories Division Attn: Librarian M/F Contract AF33(616)-3920 Princeton, New elersey Radioplane Company M/F Contract AF33( 600)-23893 Van Nuys, California Ramo-Wooldridge, a division of Thompson Ramo Wooldridge, Inc. Attn. Technical Information Services 8433 Fallbrook Avenue P.O. Box 1006 Canoga Park, California Rantec Corporation Attn: R. Krausz M/F Contract AF19(604)-3467 Calabasas, California Raytheon Manufacturing Corp. Attn: Dr. R. 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California Stanford Research T nstitute Aircraft Radiation Systems Lab. Attn D, Scheuch M F Contract AF33(616)-5584 Menlo Park, California Sylvania Electric Products, Inc. Electronic Defense Laboratory M/F Contract DA 36-039-SC-75012 P.O. Box 205 Mountain View, Talifornia Mr. Roger Battie Supervisor, technical Liaison Sylvania Electric Products, Inc. Electronic Systems Division P.O. Box 188 " Mountain View, California Sylvania Electric Products, Inc. Electric Svs terns Division Attn P Faflick M F Contract AF33(038)-21250 100 First S+reet Waltham 54. Massachusetts Tamar Electronics, Inc Attn L B McMurren 2045 w Rosecrans Avenue Gardena, California Technical Research Group M/F Contract AF33(616)-6093 2 Aerial Way Syosset, New York Temco Aircraft Corporation Attn: G. Cramer M/F Contract AF33(600)-36145 Garland, Texas Electrical Engineering Res. Lab, University of Texas Box 8026, University Station Austin, Texas A. S, Thomas, Inc, M/F Contract AF04(645)-30 161 Devonshire Street Boston 10, Massachusetts Westinghouse Electric Corporation Air Arm Division Attn: P. D, Newhouser Development Engineering M/F Contract AF33( 600)-27852 Friendship Airport Baltimore, Maryland Professor Morris Kline Institute of Mathematical Sciences New York University 25 Waverly Place New York 3, New York Dr , S. Dasgupta Government Engineering College Jabalpur, M.P, India Dr.. Richard C. Becker 10829 Berkshire Westchester, Illinois The Engineering Library Princeton University Princeton, New Jersey AF 33(616)-6079 Dr. B. Chatterjee Communication Engineering Dept . Indian Institute of Technology Kharagpur (S.E. Rly.) India Sperry Phoenix Company Attn: Technical Librarian P.O. Box 2529 21111 North 19th Avenue Phoenix, Arizonia Dr. Harry Letaw, Jr. Raytheon Company Surface Radar and Navigation Operations State Road West Wayland, Massachusetts